In the context of mathematical modeling of complex vessel tree structures with deformable models, we present a novel level set formulation to evolve both the vessel surface and its centerline. The implicit function is computed as the convolution of a geometric primitive, representing the centerline, with localized kernels of continuously-varying scales allowing accurate estimation of the vessel width. The centerline itself is derived as the characteristic function of an underlying signed medialness function, to enforce a tubular shape for the segmented object, and evolves under shape and medialness constraints. Given a set of initial medial loci and radii, this representation first allows for simultaneous recovery of the vessels centerlines and radii, thus enabling surface reconstruction. Secondly, due to the topological adaptivity of the level set segmentation setting, it can handle tree-like structures and bifurcations without additional junction detection schemes nor user inputs. We discuss the shape parameters involved, their tuning and their influence on the control of the segmented shapes, and we present some segmentation results on synthetic images, 2D angiographies, 3D rotational angiographies and 3D-CT scans. ©2011 COPYRIGHT SPIE--The International Society for Optical Engineering. Please use http://dx.doi.org/10.1117/12.878048